Cover LetterDear Editor,

We would like to re-submit the approved manuscript entitled “Who cares for the

children’s health when migration splits rural households? Evidence from a Chinese

province”. We contact editor@econmodels.com so many times during these two

years using 47189193@qq.com, when Editorial Assistant Patricia Wallace told us

our paper “has conditionally approved the publication” in Jan 22th, 2013 (please see

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Our paper explores the relationship between migration from rural villages and its affect on the status of a child’s health by analyzing the health gap between children in migrant families and non-migrant households in rural Anhui province, China.

We ues the Heckman two-step model and the Oaxaca-Blinder decomposition technique to analyze 432 samples conducted by the Chinese Academy of Agricultural Sciences. Results indicate that parental migration negatively impacts a child’s health at a statistically significant level. Furthermore, the decomposition outcome yields a health gap of 0.377 kg/m2, which demonstrates that left-behind children have poorer health than those living with two parents. A difference of 4.04% could account for differences in endowments between children in non-migrant families versus migrant families, and the gap in discrimination occupies 95.52%. This study suggests that comprehensive measures should be taken to help parents balance work and family responsibilities in order to maximize the health and development of children.

Below are our responses to your submission requirements.

• Author names and affiliations:Beibei Wu a,b*, Yongfu Chen c, Jingdong Luan d & Kaiyu Lu e

a College of Economics and Management, Nanjing Agricultural University, No.1 Weigang Road, Nanjing, 210095, P.R. China.b China Center for Food Security Studies, Nanjing Agricultural University, Nanjing, 210095, P.R. China.c College of Economics and Management, China Agricultural University, P.O.Box032, No.17 Tsinghua East Road, Haidian District, Beijing, 100083, P.R. China.d College of Economics and Management, Anhui Agricultural University, No.130 Changjiang Road, Shushan District, Hefei, 230036, P.R. China.e Institute of Agricultural Economics and Development, Chinese Academy of Agricultural Sciences, No.12 Zhongguancun Nandajie, Haidian District, Beijing, 100081, P.R. China.

• The email addresses of all authors:Dr. & Lecturer Beibei Wu, babewu@njau.edu.cn; 47189193@qq.comPro. Yongfu Chen, chenyf@cau.edu.cn; chenyf39@gmail.comPro. Jingdong Luan, luanjingdong@ahau.edu.cnPro. Kaiyu Lu, lky_lv@163.com

• *Corresponding Author.E-mail addresses: babewu@njau.edu.cn; 47189193@qq.comTelephone and fax numbers: (+86) 13914771410Full postal address: No.1 Weigang Road, College of Economics and Management, Nanjing Agricultural University, Nanjing, 210095, P.R. China.

Finally, this paper is our original unpublished work and it has not been submitted to any other journal for reviews.

Sincerely yours,

Beibei WuCorresponding author

Title page

Title: Who cares for the children’s health when migration splits rural households? Evidence from a Chinese province

Corresponding Author: Dr. Beibei WuCorresponding Author's Institution: Nanjing Agricultural UniversityE-mail addresses: babewu@njau.edu.cn; 47189193@qq.comTelephone numbers: (+86) 13914771410Full postal address: No.1 Weigang Road, College of Economics and Management, Nanjing Agricultural University, Nanjing, 210095, P.R. China.

First Author: Bei-bei Wu, Doctor

Order of Authors: •Beibei Wu a,b*, Yongfu Chen c, Jingdong Luan d & Kaiyu Lu e

a College of Economics and Management, Nanjing Agricultural University, No.1 Weigang Road, Nanjing, 210095, P.R. China.b China Center for Food Security Studies, Nanjing Agricultural University, Nanjing, 210095, P.R. China.c College of Economics and Management, China Agricultural University, P.O.Box032, No.17 Tsinghua East Road, Haidian District, Beijing, 100083, P.R. China.d College of Economics and Management, Anhui Agricultural University, No.130 Changjiang Road, Shushan District, Hefei, 230036, P.R. China.e Institute of Agricultural Economics and Development, Chinese Academy of Agricultural Sciences, No.12 Zhongguancun Nandajie, Haidian District, Beijing, 100081, P.R. China.

• The email addresses of all authors:

Dr. & Lecturer Beibei Wu, babewu@njau.edu.cn; 47189193@qq.comPro. Yongfu Chen, chenyf@cau.edu.cn; chenyf39@gmail.comPro. Jingdong Luan, luanjingdong@ahau.edu.cnPro. Kaiyu Lu, lky_lv@163.com

Who cares for the children’s health when migration splits rural households? Evidence from a Chinese province

Abstract

The study explores the relationship between migration and children’s health by analyzing the health gap between children in migrant and non-migrant households in rural Anhui province, China. The study adopts the Heckman two-step model and the Oaxaca-Blinder decomposition technique to analyze 432 samples. We find that parental migration negatively affects the outcome of a child’s health and yields a health gap of 0.377 kg/m2. 4.04% could account for differences in endowments between children in non-migrant versus migrant families, and the gap in discrimination occupied 95.52%. Our evidence demonstrates that comprehensive policies should be taken to improve migrant children’s health.

JEL classification: I14; I18; I38

Keywords: Migration; Children health; Rural China; Heckman two-step model; Oaxaca-Blinder decomposition technique

1. Introduction

China is experiencing an economic transition period because of the accelerated development of industrialization and urbanization; consequently, there has been an imbalance in regional development. The large-scale migration from the countryside to the city (World Bank, 2009) has created complex social problems that the society must deal with to avoid major problems. Chief among these problems is the fate of the children left behind in the care of people other than their parents. Chinese farmers have moved to cities in an attempt to make a better living; they have become the backbone of the industrial labor force. However, their children are in their rural villages; this often-neglected group is known as “left-behind children1” (de Brauw & Mu, 2011). From the situation of some other developing countries without the hukou (i.e., household registration) system, the migration itself is also an uncertain behavior with high risks (Mallee, 1995). Problematically, the migrants either cannot emigrate with the whole family or overcome the limitations of poor rural living standards, inadequate cash resources, and long work hours leaving parents have insufficient time to take care of their children. International mobility to nonagricultural employment is also limited for many poor rural farmers living with their children (Beine, Docquier, & Rapoport, 2008). Hence, the problem of left-behind children is a social problem not only in rural China, but also is a common problem of rural labor migration in many other developing countries with economies in transition (Stark & Taylorje, 1991).

Research on migrants in rural China has indirectly provided information on the reasons for children being left behind. Government systems are considered as the most important factors influencing the fair treatment of rural-to-urban migrant workers and their children. These systems include the hukou system and the compulsory education finance investment system, which create formidable barriers between the rural and urban segments of society (Mallee, 1995). Hukou reforms since the late 1980s have stimulated the flow of migrant laborers out of rural China as labor market restrictions were loosened. Once migrants obtain temporary residency, they are better able to search for jobs with higher wages in the labor markets (Munshi, 2003). However, legal temporary residence status prevents entire households, particularly those with children, from

1 People call them “left-behind” children, meaning that one or both parents are working far away from home for more than six months and rarely spend time to care for their sons or daughters in school. These children are usually taken care of by only one of their parents, their grandparents, or other relatives.

moving to the urban areas; furthermore, temporary residence status does not allow access to the same social benefits as urban residents. In spite of reforms in temporary residence status, the vast majority of peasant migrants are still largely barred, legally or financially, from accessing public education for their children in the city, and thus prevented from bettering their employment and treatment, increasing their social security and welfare and improving their housing conditions. The migrants continue to be bogged in inferior institutional, economic and social positions compared to urban residents (de Brauw, 2011). For example, the number of migrant children in schools is equally hard to judge as urban children. Non-residents are either denied access or face extra charges, such as huge Jiedufei (i.e. sponsorship fees) in urban public schools. Migrant parents worry about the quality and management of migrant schools. Furthermore, the restrictive public school policy and the hukou system restrict their children by creating barriers to the entrance exams. Therefore, as more and more rural residents migrate for work, the number of children left behind at home is increasing. These problems are the direct results of the dual economic and political system, which prevent farmers from being included in the employment system (Cai, 2003).

Children are left behind not only because of the hukou system, but also because of the extreme poverty of the migrants (Zhang, Brauw, & Rozelle, 2004). Cai (2003) further argue that the discriminatory treatments of the rural-to-urban migrant laborers are in terms of children’s expensive school fees, the increase in the cost of living, and migrant workers having inadequate energy to take care of their children. Hence, we see the creation of a special community: the “left-behind children”.

Under the context of increasing awareness of the problems of the left-behind children, more attention is being paid to evaluating the relationship between parental decisions to migrate and their children’s health status (Schmeer, 2009). Does parental migration lead to better or worse outcomes for these children? Existing studies have found conflicting results regarding the effect of migration on children’s health. Some researchers hold that a migrant may send home amount of money higher than the wages he could have earned at home and may be more likely to invest more resources in children’s health. In addition, the extended families have successfully taken care of children left behind. These studies have showed positive effects of migration on the health of rural children (Mansuri, 2006). On the other hand, other investigators have provided evidence of negative effects of migration on children. These children have a relatively low level of nutrition, inadequate diet, and higher morbidity rates (Nobles, 2007). They also demonstrate that even if the presence of other adults is a common occurrence in migrant households, children may still suffer from the absence of their parents. Therefore, findings of a robust relationship between migration and children’s nutritional status could have important policy implications for urbanization in China.

Most of the studies in migration literature focus on labor and work-related movement that improves incomes and modifies risk (Macours & Vakis, 2010). However, little attention has been paid to the relationship between parental migration and their children’s health outcome, and rarely considered the decomposition technique to compare healthy differences in children left behind and children living with parents. In aggregate, previous studies have contributed to some understanding of China’s migrants in relation to human capital investments for children (de Brauw & Mu, 2011). Nevertheless, it seems that no one could reach a common ground.

In our paper, due to omitting observations with missing information and truncated observations, we use the Heckman two-step model to avoid sample selection bias (Heckman, 1974). Based on this, to examine whether parental migration will cause a decrease in the health status of their children, we also apply the Oaxaca-Blinder decomposition technique (Oaxaca, 1973; Blinder, 1973), which is widely used to identify group differences, including racial and gender gaps, in outcomes.

The purpose of this paper is to analyze the correlation using anthropometric health measurements (body mass index) and the differences in left-behind children’s health in comparison to children living with both parents.

2. Hypothesis

Peng (2005) points out that heredity and environment are both main factors for children’s physical development. Nutritional status is the most fundamental and important factor among the environmental factors that influence children’s physical development and can be used as an appropriate index to estimate children’s physical development (Chen, 2009). We can construct a body mass index (BMI) to define overweight and underweight status that is recommended by WHO (Freedman et al., 2005; de Brauw & Mu, 2011). Adults with a BMI over 25 are considered overweight, and adults with a BMI over 30 are considered obese, whereas adults with a BMI below 18.5 are considered underweight. Children, however, have a different distribution of body weight. We apply both the definition from the Group of China obesity task force correspondence & Ji’s (2004) work, which used samples from around China to construct a gender and age specific set of BMIs. Therefore, we can adopt BMI to estimate the health status of children left behind. BMI is calculated by dividing a person’s body weight in kilograms by their height in meters squared. The BMI can be described as follows:

BMI=Weight (kg )/ Height (m2 )

(1)

This study conducted a questionnaire survey of left-behind children and then compared outcomes for the reference children in non-migrant households in three counties (Wuwei, Feidong and Guoyang) of the Anhui Province in rural China. During the research, we gave the left-behind children medical examinations and measured their height and weight. Medical professionals conducted medical examinations carefully and to ensure accurate measurements. All of the children were assigned to groups before the physical examination, and each group was assigned to a professional. Additionally, the measuring instruments were calibrated before the examination of each child so that we could get an accurate BMI index from every child.

The survey presents information not only for the indicator of a child’s physical health, but also for the family’s health, children’s demographic characteristics, school aspects and regional characteristics. At the family level, we analyzed indicators including whether the parents were going out for work or not, the parents’ physical condition, mother’s educational level and household monthly per capita consumption. The left-behind children living in single-parent family or entrusted to grandparents and relatives may have a different quality of life with a higher malnutrition rate compared to normal children in non-migrant households (Nobles, 2007). Genetic factors have an important influence on a person’s height and obesity; therefore, the parents’ physical condition will directly affect a child’s health. Moreover, a well-educated mother’s behavior will have a major impact on her children. The household’s monthly per capita consumption level will also have a great influence on the health of the child. Rich families can provide necessary nutrition and health care to their children, thereby, promoting their physical health (Smith, 1999).

We also selected the indicators of a child’s dietary habits to include having breakfast and cognitive scores of nutritional knowledge for the demographic characteristics. Good eating habits can help children improve their physical fitness and maintain good shape. Nutrition not only provides the energy consumed during exercise, but also repairs a person’s body and enhances human health. Moreover, children with a basic knowledge of healthy nutrition may pay more attention to their eating habits, which has a positive effect on their own health outcome.

The main school factor we analyzed is physical education. Because some schools do not attach importance to physical education, the classes are usually overwhelmed by cultural courses. Although physical exercise can enhance physical fitness, most students lack interests in sports and physical exercise. This can directly lead to the significant decline of children’s physical indicators.

We also selected a regional factor as a variable, which may have a significant influence on children’s physical health because geographical environment and economic development are different among different regions.

As stated above, we propose the following hypothesis: a child’s health status is determined by many different factors and parents going out to work may cause changes in living habits of the children and affect their physical health. Hence, we insist that immigrant parents may have a

negative effect and statistical significance on their children’s physical health.

3. Data

3.1. Selection method of surveyed sample

Our analysis is based on field interviews and questionnaire surveys conducted by the Chinese Academy of Agricultural Sciences in 2007 in the rural area of Anhui province, China. We designed four kinds of questionnaires in terms of the children themselves and their corresponding households, schoolmasters and village leaders. The survey provided adequate data for analyzing the rich socioeconomic information of individuals, households, schools and communities in the sample.

For the selection of the surveyed sample, the interviews were conducted in three counties (Wuwei, Feidong and Guoyang), located in three of Anhui province districts (i.e., from south to north). Such locations were chosen to ensure a sample representative of a cross-section of the Anhui population and to avoid potential selection bias from individual sampling. Then in each county, we chose two towns randomly and three kinds of schools (the town’s junior school, the town’s main elementary school and the entire village’s elementary school) randomly in each town. Next, in each school, we picked out three grades and chose one class randomly. Using the method of stratified sampling, we divided all the children in one class into two kinds: left-behind children and the reference children in non-migrant households. In this sample, eight sample children were randomly selected in every class as appropriate parties to be involved with the investigation. In this way, we chose 2 sample towns in each county, and got 6 sample towns in all; 3 sample schools in each town, and got 18 sample schools. Then in each sample school, we investigated 24 sample children with questionnaires. Overall, we sampled a total of 432 children and received 432 valid questionnaires. Accordingly, we interviewed the corresponding households, schools and communities and retrieved those questionnaires.

The respondents were children between the ages of 8 and 18 in schools attempting to accomplish nine-years of compulsory education. Roughly 47.7% of the entire sample is male students. Left-behind children hold a greater proportion (about 57.87%) in the sample, with male students accounting for 49.20%.

From the rural distribution, our sampling survey covered 71 villages (either towns or communities) and left-behind children were living in 57 villages, with the reference group distributed in 48 villages. The investigation was carried out in a population of 112 (a sample fraction of 25.93%) for left-behind children only living with one parent and 138 (a proportion of 31.94%) for children living without both parents (Table 1).

Table 1

The situation of parental / non-parental migration in the sample.

Observation Percent (%)Cumulativepercent (%)

182 42.13 42.1399 22.92 65.0513 3.01 68.06

138 31.94 100432 100

Both parental migrationTotal

Groups

Non-parental migrationMigration of the fatherMigration of the mother

Source: The data are obtained from the questionnaire by statistical processing of the authors.

As shown in Table 1, migration rates are higher for men than women in rural China when analyzing left-behind children living with one parent. The household in most cases is one where the mother stays at home and father goes out to earn money. The traditional concept of gender is built on the different characters of males and females and the arrangement of social roles. In general, mothers remain in charge of childrearing despite their active participation in the work

force and the increased sharing of domestic responsibilities. In our investigation, children were left behind in the care of a single parent, grandparents or other relatives. Additionally, some parents leave home to find work in the cities and they are able to leave their children behind by increasing financial support while the relatives sometimes care for the children. Among those 250 left-behind children, 49% were living with one parent. Moreover, 55.2% of these children were left behind by both parents with 98% of them raised by their grandparents and 5.3% raised by other persons.

3.2. Data and sample characteristics

In our sampling survey, we introduced the measures used for children’s BMI and divided children’s health outcomes into these three levels2 (Group of China obesity task force correspondence & Ji, 2004; Peng, 2005). As can be seen in Table 2, there are 278 observations for rural children with malnutrition, which accounts for 645%. Among the 432 children, 136 are in good health status and 18 are in the condition of overnutrition, only occupying 27%. In our investigation, we found that the obese children existed in different kinds of families, no matter whether their parents had migrated or not. If children have good genes, the risk of becoming obese is very small, because childhood obesity is often related to a hereditary factor. Hence, we dropped 18 observations with a BMI value greater than normal nutrition level among the children.

Table 2

The status of the children’s physical health.

Observation Mean Standard deviation Min MaxMalnutrition 278 16.13 1.57 11.48 19.38

Normal nutrition 136 18.96 1.33 15.26 21.78Overnutrition 18 22.86 2.17 19.53 26.64

Children’s health status (BMI)Health levels

Source: The data are obtained from the questionnaire by statistical processing of the authors.

Before we present an empirical strategy for identifying potential linkages between migration and health status among children, we first discuss the data set regarding the household, individual and school levels in more detail. Additionally, we considered the community factor to examine the influence on children’s health outcomes. All of the selected explanatory variables are presented in Table 3 with their statistical descriptions and their expected signs, which will affect the dependent variable. The sample statistics indicate that our selected sample is representative of most of the characteristics of the population in the study area. According to the statistical description of the variables, the dependent variable is analyzed as every child’s BMI. In general, the mean of children’s BMI in the sample was 17.30 kg/m2 (Table 3).

At the household level, we examined not only the impact of migration (Outwork) on the health of children, but also the influence on Fbmi, Mbmi, Medu and Cost. Outwork is the main indicator variable, taking on the value of one if one or both parents had migrated in 2006. If one or both parents migrated, the remaining household members may have to take on all of the tasks such as child rearing, cooking, and other household tasks (World Bank, 2009). In particular, less time may be allocated to either cooking or monitoring the eating habits of children, which leads to their malnutrition status. Therefore, we assumed that the expected sign of Outwork is negative.

Fbmi and Mbmi are included in the model to capture the effects of the parents’ log BMI on the health status of their children. All previous studies, either descriptively or empirically, have found that parents’ BMI is a positive influence on children’s physical health (Peng, 2005).

This model also includes Medu, which is a dummy variable. The value of Medu is one if the education of mother is at the level of primary school or illiteracy. In general, more educated mothers may have healthier children because they have better knowledge about health care, and

2 According to the standard of demarcation of Ji (2004) & Peng (2005), we divide children’s BMIs into three levels, which are: (1) malnutrition which equals < P80 (1-10%); (2) normal nutrition which equals P80 (1-10%) ~ P80 (1+10%); and (3) overnutrition which equals > P80 (1+80%). The 80th percentile of BMI distribution is represented as the median of Height / Weight.

provide more sanitary and safer environments for their children (Hartog & Oosterbeek, 1998). Thus, the estimate for Medu is expected to be positive.

The model includes Cost, which indicates the log expenditure of a family’s monthly per capita income. According to Case & Paxson (2001), families with high consumption ability are more able to provide a clean living environment, healthy food with higher quality, and good medical care measures. Moreover, the parents can care more about the health and nutrition of children (i.e., diet, sanitation, and safety). Therefore, the estimate for Cost is expected to be positive.

At the children’s level, the two variables of Breakfast and Score are included in the model. Breakfast is a dummy variable that equals one if a child has breakfast every day. We presume the expected sign to be positive. Then, the level of children’s health knowledge (Score) is included in the model as a continuous variable. If the children’s nutritional knowledge is relatively low, they are not aware of the health problems that are caused by micronutrient deficiency. Hence, the estimate for Score is expected to be positive.

Table 3

Statistical characteristics of selected variables.Variable Description, unit Mean Standard

deviationMinimum Maximum Expected

signDependent variable

Non-overweight (yes=1) 0.96 0.2 0 1

Children’s body mass index (kg/m2) 17.30 2.32 11.48 26.64Independent variablesHousehold characteristic Outwork Whether one or both parents had migrated out to work or not in 2006 (yes=1) 0.58 0.49 0 1 - Fbmi Natural logarithm value of father’s body mass index 3.12 0.11 2.76 3.48 + Mbmi Natural logarithm value of mother’s body mass index 3.09 0.12 2.77 3.50 + Medu Mother’s educational level (primary school or illiteracy=1) 0.21 0.41 0 1 + Cost Natural logarithm value of household monthly expenditure per capita 4.90 0.71 2.41 7 +Demographic characteristic Breakfast Whether children have breakfast or not everyday（yes=1） 0.75 0.43 0 1 + Score Score of children’s health knowledge (points) 75.58 23.90 0 100 +Scholastic characteristic PE The frequency of children having physical exercises in a week（times） 2.50 2.72 0 20 +Regional characteristic Feidong Feidong county (yes=1) 0.33 0.47 0 1 ? Guoyang Guoyang county (yes=1) 0.33 0.47 0 1 ? (Wuwei) Wuwei county, the reference group (yes=1) 0.33 0.47 0 1

Bmi

Source: The data are obtained from the questionnaire by statistical processing of the authors.

In terms of the scholastic characteristics, we select the PE variable to capture the effects of the frequency of having physical exercises in a week on the child’s health status. This is because children in school need sports and activities to increase their physical health and to relax; however, in some schools, they are not given enough time to do outside activities in our sampled locations. The estimated sign for PE is thus also expected to be positive.

Lastly, a dummy variable denoting the different regions is also included in our model to present the effect on children’s health outcomes. The children’s physical health is restricted and different, which to some extent is because of geographical and social economic scales. We select three sample counties from south to north in Anhui province, because the South and North are different in lifestyle, climate, and dietary habits. For example, a staple food in the South is mainly rice, and foods in the North are generally made from flour. Thus, the expected sign is not easy to be determined. We chose Wuwei County as the reference group.

4. Methodology

4.1. Heckman two-step model

Although the samples were almost evenly distributed across the three locations, restricting the survey to Wuwei, Feidong and Guoyang counties in Anhui province may have caused sample

selection bias. At the same time, we truncated 18 samples of obese children, which accounts for 27% of the overall total sample (Table 2). This is because overweight children are, to some extent, linked to genetics. Sample selection decisions by either investigation or data processing operate in much the same fashion as self-selection, so we use the Heckman two-step model (Heckman, 1974) to avoid potential selection bias from individual sampling.

There are two steps in Heckman estimation. The first step involves estimating the parameters in Eq. (2) by the probit model, using the entire sample. These estimates can then be used to compute the inverse of Mill’s ratio (i.e., IMR), λ for each individual in the sample. Once λ is computed, we can estimate Eq. (3) over the sample of non-overweighed children by ordinary least squares regression (i.e., OLS regression), treating ρ as the regression coefficient forλ . Heckman’s two-step model can be described as the following equations.

The selection equation is

s=1

if zγ+u>0

(2)

The regression equation is

y=xβ+λρ+η (3)

where

u ~ N (0,1)

η ~ N (0 , σ ) (4)corr (u ,η )= ρ

that is, u and η , are mean-zero stochastic errors representing the influence of unobserved

variables affecting s and y which are both under the assumption of a bivariate normal distribution; y is the observed health status for individual i if the child is not obese; Both z and x are vectors of observed explanatory variables, and x should be a strict subset of z , implicating

that we have at least one element of z that is not also in x (Wooldridge, 2002); γ and β are

unknown parameters; λ is given by

λ (c )=φ(−c )Φ (c )

(5)

wherec=zγ ,φ andΦ are the density and distribution functions of the standard normal distribution, respectively.

Once the variable of IMR is inserted in the initial model, two factors can be evaluated to help determine whether there is significant bias resulting from the missing responses (Anne et al., 2004). First, one can examine the significance of the IMR variable itself. If it is significant, it suggests that there is a significant bias in the initial model. However, the IMR may be weaker than expected, and this method may be limited in its ability to detect bias. Therefore, the other factor to examine, following the addition of the IMR variable into the original regression model, is whether or not there have been significant changes in any of the parameter estimates of the other predictor variables in the model. Changes in parameter estimates of > 10% may indicate that these estimates were biased due to missing surveys (Anne et al., 2004).

The expected value of y , conditional on z ands=1 , can be written as the following,

E( y|z , s=1)=xβ+ρλ ( c )

(6)

If x is a continuous variable, the partial effect of the expected value of y with respect to x is,

∂ E( y|z , s=1)∂ x

=β−ργλ (c )[ c+ λ(c )] (7)

Multiplying both sides of Eq. (7) by x / E( y|z , s=1 )and simplifying, the elasticity of the expected value of y with respect to x can be expressed as,

ε cond=∂ E ( y|z , s=1 )

∂ xx

E ( y|z , s=1) (8)

If

x

is a binary variable, then the difference of

E( y|z , s=1)

at

x i=1

and

x i=0

is the estimated partial effect.

4.2. Oaxaca-Blinder decomposition technique

The Oaxaca-Blinder decomposition technique attributed to Oaxaca (1973) & Blinder (1973) is widely used to identify and quantify the separate contributions of group differences in measurable characteristics, such as education, experience, marital status, and geographical differences to racial and gender gaps in outcomes (Fairlie, 2002). The procedure divides the differences between the two groups into a part that is “explained” by group differences in characteristics such as work experience and a residual part that cannot be accounted for by such differences in determinants. This “unexplained” part is often used as a measure for discrimination, but is also subsumes the effects of group differences in unobserved predictors. In general, the technique can be employed to study group differences in any (continuous and unbounded) outcome variable (Ben, 2008). For example, O’Donnell et al. (2008) utilize this technique to analyze health inequalities due to poverty status.

According to the theory of this decomposition technique, we conducted a comparative study to examine healthy differentials between the left-behind children group and the control children group whose parents are living and working in the home.

The linear regression model in Eq. (6) is estimated separately for the groups g=( A ,B ). For these models, the mean outcome of healthy difference can be expressed as:

R=Y A−Y B=X i

A αiA−X i

Bα iB

(9)

where α i

is considered to be the regression coefficient for X i

; A

and B

denotes the left-behind

children group and the control children group, respectively; Y

is the sample mean of the outcome

variable (i.e., BMI); X i

is the mean of the vector of regressors (i.e., Outwork, Cost, etc.); and Y A−Y B

represents the mean outcome difference between group A

and group B

.

Then, Eq. (9) can be decomposed as:

R=∑i=1

n

( X iA−X i

B)×αi¿+[∑

i=1

n

X iA (αi

A−α i¿)+∑

i=1

n

X iB(α i

¿−αiB) ]

(10)

where the first term on the right-hand side of Eq. (10) displays the differences in the outcome variable between the two groups A and B due to differences in observable characteristics or differences in endowments explained part of the differences in health. The second term shows the differential that occurs because of differences in the estimated coefficients; in other words,

differences in discrimination are treated as the unexplained part. Finally, α i¿

is a set of benchmark

coefficients (i.e., the coefficients from the non-discriminatory structure). In general, α i¿=αi

A or

α i¿=αi

B (Oaxaca, 1973; Blinder, 1973).

5. Results

5.1. Results of Heckman two-step model

As stated in Section 4, missing data from survey participants can cause sample selection bias in parameter estimates of the models’ predictive outcomes. Unfortunately, regression models are frequently interpreted with the assumption that the available data are representative of the entire study population. Therefore, we use the Heckman two-step model to assess and control for bias due to truncating 18 samples of obese children and the limitation of the data.

This method has two steps. The first step is the development of a selection equation (i.e., a probit model of factors associated with all of the 432 samples in our survey) that estimates whether or not all the children are non-overweight. This includes deriving an individual variable from the selection equation called the IMR. In this study, the value of the IMR for each child represents the predicted probability that they are not overweight. The second step of the Heckman method is the insertion of the IMR variable into the initial regression model (i.e., the model not accounting for potential bias due to missing information) from a given study in order to assess for, and attempt to control for, selection bias. With these factors taken together, the insertion of the IMR variable into the initial risk models does not allow for the assessment of whether or not there is bias in the initial models, which would suggest that the initial predictors are mostly associated with biasness (Table 4). Furthermore, although the parameter estimate in the IMR variable itself was not statistically significant, we can still use this estimation to analyze the impact of out-migration on the children’s health status.

The final multivariable model (after the addition of the IMR variables from the Heckman two-step model) is presented in the third column of Table 4. There was little evidence of selection bias for the extended OLS model. The estimated empirical results showed that all parameters were given the expected signs, except the Breakfast parameter. The parameters of Outwork, Fbmi, Breakfast, Feidong and Guoyang were statistically significant in the extended OLS model, implying that all of our hypotheses about the independent variables’ influences on a child’s health status were empirically demonstrated; but, the empirically estimated coefficients for the variable factors of Cost and Score was not statistically significant.

As shown in the regression equation in Table 4, the partial effect with respect to Outwork was negative at a 10% significance level related to the outcome of a child’s health. The marginal effect with respect to Outwork was -0.354, indicating that the left-behind children from eight to eighteen years of age in our sample had poorer health, with a gap of 0.354 kg/m2 than those living with two biological parents in 2007. The possible reason may be that children left behind by their parents are usually taken care of by their grandparents or other relatives. These adults supervising the children can only take care of a child’s personal safety and daily living and are unable to care for the child’s daily diet. For a single parent in a migrant household, it is possible that he or she often undertakes more farm and household production and are therefore not responsible for child rearing, and the child is often left to grow on their own (Mu & van de Walle, 2009).

The parameter of Fbmi (i.e., log father’s BMI) was positive at a 1% significance level, impling that the health status at the child level was more strongly associated with their fathers’ health status. The results were consistent with the findings related to the study by Peng (2005). As shown in Table 4, a one-unit increase in father’s BMI led to a 0.110 kg/m2 increase in the health status of

the children. Moreover, a 10% increase in father’s BMI resulted in a 1.467% increase in their child’s health status.

The empirically estimated coefficient for Cost was positive, but did not significantly result in a change in the health of a child. The possible reason may be that the level of local social economy is comparatively lower and it is located in the country of China. For example, the average monthly family expenditure was 173.36 Chinese yuan per capita (not including the autarky in the farmer’s home or that the farmer grew food on his land and ate it) in 2006. The lowest and highest expenditures in the sample were 11.11 Chinese yuan and 1250 Chinese yuan. In our investigation, 378 households (i.e., a proportion for 87.5%) lived on less than 300 Chinese yuan per capita per month. The empirical results showed that a 100 Chinese yuan increase in the expenditure of the household per capita raised the health status among children by 0.002 kg/m2. Furthermore, a one-fold increase in household expenditure only led to a 0.014% increase in children’s BMI.

The Breakfast variable was negatively linked to children’s health status at the 5% significance level. But the sign of the coefficient was not in accordance with our expectation. One plausible, but empirically less tractable reason could be that the traditional, everyday diet of local people in the three sample counties is a simple affair that includes vegetables, cucumbers and beans for three meals. The households with a low level of wealth have limited resources, such as living expenses and human capital investment, and cannot afford purchasing nutritional food due to the economic disadvantages. Additionally, the health outcome of children in our investigation areas is not promising; indeed, the representative sample of children with normal health status accounts for 31.48%. As shown in Table 4, the marginal effect of Breakfast was -0.486, indicating that the gap between children who have breakfast everyday or not was 0.486 kg/m2.

The estimated results of the Score variable indicated that a one-unit increase in Score produced a 0.004 kg/m2 increase in children’s health outcome. Finally, the elasticity with respect to Score was 0.0185, implying that a 10% increase in Score caused a 0.185% increase in children’s BMI.

For the aspects of regional characteristics, the regional variable was highly sensitive to health status among children. From the empirical results, a significant (P<0.01) Feidong coefficient and a significant (P<0.05) Guoyang coefficient implied negative effects of health status among children, compared to the reference group of Wuwei County. The possible reasons for these results may be the influence of macroeconomic and financial situations in the surveyed region. The estimated marginal effect showed that the BMI indicator among children in Feidong and Guoyang were much lower than that in Wuwei, and the health gaps were 0.916 kg/m2 and 0.563 kg/m2, respectively.

Table 4

Results of the Heckman two-step model.

Selection Eq. Regression Eq.

Outwork -0.0828 (0.2507) -0.3544 (0.2011)* -0.35445 (0.20109) Fbmia -2.0923 (0.9889)** 2.4663 (0.8957)*** 0.10983 (0.01211) 0.14665 (0.01799)

Mbmia -0.8542 (1.1047) Medu 0.7275 (0.3581)** Costa 0.1909 (0.1937) 0.0024 (0.1465) 0.00002 (0.00002) 0.00014 (0.00002) Breakfast -0.2344 (0.3065) -0.4864 (0.2269)** -0.48638 (0.22693) Score 0.0103 (0.0052)** 0.0041 (0.0041) 0.00409 (0.00410) 0.01848 (0.00612) Pe -0.0566 (0.0329)* Feidong 0.0563 (0.2894) -0.9155 (0.2466)*** -0.91552 (0.24657) Guoyang 0.3020 (0.2606) -0.5630 (0.2336)** -0.56302 (0.23363) IMR 0.7297 (0.7047)

Obs 432 414SigmaLog pseudolikelihoodChi-square (Wald test)Prob﹥chi2

Marginal effect(∂ E(y | z, s=1) /∂ x)

Elasticity(εcond)

1.9461 (0.0695)-914.2878

0.000036.09 (7)

Heckman two-step model Independent variables

Robust standard errors are shown in parenthesis. ***, ** and * denote statistically significant at the 1%, 5% and

10% level, respectively. “a” indicates the variable is taken its natural logarithm value, and its partial effect and elasticity can be obtained by taking the exponential value of the variable on the right-hand side of Eq. (7) and Eq. (8), respectively.

5.2. Results of Oaxaca-Blinder decomposition estimation

Based on the extended OLS Heckman two-step model, the standard application of the Oaxaca-Blinder decomposition estimation is to divide the health gap between children in migrant households and non-migrant households into a part that is explained by differences in determinants of BMI and a part that cannot be explained by such group differences. The decomposition output reported differences are in Table 5. In our sample, the mean of the BMI dependent variable is 16.906 kg/m2 for left-behind children and 17.282 kg/m2 for the reference children living with both parents in the home, yielding a health gap of 0.377 kg/m 2, which is the sum of column 2 and column 4 in the last row in Table 5. The result was consistent with the finding related to the extended OLS model (i.e., with the empirically estimated coefficient for Outwork of 0.354 kg/m2) in Table 4.

According to Eq. (9) in the decomposition output, the increase of 0.0152 in the sample indicated that differences in endowments accounted for about 4.04% of the health gap between children in non-migrant families and children left behind in migrant families. The increase of 0.3613 in Table 5 illustrates that the gap in discrimination, as an unexplained part, occupied 95.52%. The decomposition outcome shows that the discrimination of health status was only directed against left-behind children and that the reference children living with both parents face no discrimination. To improve the situation of left-behind children can, to a certain extent, promote their health status.

Table 5

Results of Oaxaca-Blinder decomposition estimation.

Characteristics(Endowments)

Percent (%)Coefficients

(Discrimination)Percent (%)

Fbmi -0.0160 (0.0311) -4.25 -0.0788 (5.3918) -20.93 Cost -0.0036 (0.0231) -0.96 -3.4515 (1.3265)*** -916.71 Breakfast -0.0298 (0.0242) -7.92 0.0957 (0.3434) 25.42 Score 0.0110 (0.0158) 2.92 -1.5264 (0.5987)* -405.41 Feidong 0.1120 (0.0509)** 29.76 0.1378 (0.1529) 36.60 Guoyang -0.0582 (0.0361)* -15.47 -0.0699 (0.1620) -18.56

Constant 0 0 5.2544 1395.55 Total 0.0152 4.04 0.3613 95.96

Robust standard errors are shown in parenthesis. ***, ** and * denote statistically significant at the 1%, 5% and 10% level, respectively.

6. Discussion

In this paper, we have examined the relationship between migration and health status among children, and divided the health gap between children in migrant households and non-migrant households in Anhui province of China, using the Heckman two-step model and the Oaxaca-Blinder decomposition technique. The data included a 432 sample conducted by the Chinese Academy of Agricultural Sciences in 2007. The main findings of this study are as follows.

First, as a suggestive explanation for this finding, we showed that parental migration was negatively related to the outcome of children’s health at a statistically significant level. Fathers usually do more exercises, and know much about improving children’s good habits and actions.

Furthermore, rich families can afford medical care, more nutritious foods, and provide a better environment for their children; therefore, their children are healthier. The traditional everyday diet of local people in the three sample counties is simple and included vegetables, cucumbers and beans for three meals, which was negatively linked to children’s health status at the 5% significance level. In addition, there is much known about the health knowledge that focuses on promoting an increase in the child’s understanding of the importance of healthy food intake at all times and other health issues. Due to the differences in regions, children’s health indicators in Feidong and Guoyang were much lower than that in Wuwei.

Second, both of the methods prove that the left-behind children have poorer health than those living with two biological parents (i.e., with a gap of 0.354 kg/m2 for Heckman two-step model and a difference of 0.377 kg/m2 for the Oaxaca-Blinder decomposition technique). 4.04% of this health gap could be accounted for by differences in endowments between children in non-migrant families versus migrant families. In addition, the gap in discrimination as an unexplained part of the health gap occupied 95.52%. The decomposition outcome indicated that the discrimination of health care was only directed against left-behind children and that there is no discrimination against children in non-migrant households.

Although we cannot make causal inferences using our investigated data, the results in this study still have important policy implications. In the context of China, where one or both parents are likely to continue to migrate and leave their children behind at home, it is important to better understand the effects of migration on the physical health of the children because their health intensely promotes the construction of the new socialist countryside.

As discussed above, government should make certain prevention measures to strengthen the children’s health education and nutritional intervention, by formulating corresponding policies and regulations to enhance the popularization of nutritional knowledge. Meanwhile, great attention should be paid to dietary habits with a focus on improving the breakfast practices and forming healthy behaviors of school students. In recent years, there have been a number of small pilot projects that have experimented with reforms to the hukou system in the Chinese cities of Chengdu, Chongqing, Wuhan and parts of Guangdong and Zhejiang provinces. China should gradually change the current hukou system in stages to allow free migration and let peasant workers and their children have equal rights with urban residents. For the migrant, a change in the social public welfare and their children’s education system would make it easier and fairer for them to obtain a job from which they can earn more. After being treated fairly in the job market, the wealth gap would narrow. Finally, government should increase the income of returning migrant farmers and loosen the labor market to encourage them to take up jobs in local enterprises or start their own businesses. In future research, more attention may be focused on helping parents balance work and family responsibilities to improve the health and development of migrant children.

Acknowledgements

The study was sponsored by “A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), and the Fundamental Research Funds for the Central Universities of China (No. SK2014035).

References

Anne, E.S., Mary, E.P., David, J.M., John, A.S., & John, S.R. (2004). Assessing response bias from missing quality of life data: the Heckman method. Health and Quality of Life Outcomes, 9, 1-10.

Beine, M., Docquier, F., & Rapoport, H. (2008). Brain drain and human capital formation in developing countries. Economic Journal, 118, 631-652.

Ben, J. (2008). A stata implementation of the Blinder-Oaxaca decomposition. ETH Zurich Sociology Working Paper No.5.

Blinder, A.S. (1973). Wage discrimination: reduced form and structural estimates. The Journal of

Human Resources, 8, 436-455.Cai, F., & Wang, D.W. (2003). Migration as marketization: what can we learn from China’s 2000

census data?. China Review, 3, 73-93.Case, A., & Paxson, C. (2001). Mothers and others: who invests in children’s health?. Journal of

Health Economics, 20, 301-328.Chen, J. (2009) Identifying non-cooperative behavior among spouses: child outcomes in migrant

sending households. Working paper, the Ohio State University.de Brauw, A., & Mu, R. (2011). Migration and the overweight and underweight status of children

in rural China. Food Policy, 36, 88-100.Fairlie, R.W. (2002). Race and the digital divide. University of California, Santa Cruz Working

Paper.Freedman, S., Khan, L., Serdula, M., Dietz, W., Srinivasan, S., & Berenson, G. (2005). The

relation of childhood BMI to adult adiposity: the Bogalusa Heart Study. Pediatrics, 115, 22-27.

Group of China obesity task force correspondence, & Ji, C.Y. (2004). Body mass index reference norm for screening overweight and obesity in Chinese children and adolescents. Chinese Journal of Epidemiology, 25, 97-102 (in Chinese).

Hartog, J., & Oosterbeek, H. (1998). Health, wealth and happiness: why pursue a higher ducation?. Economics of Education Review, 17, 245-256.

Heckman, J. (1974) Shadow prices, market wages, and labor supply. Econometrica, 42, 679-693.Macours, K., & Vakis, R. (2010). Seasonal migration and early childhood development. World

Development, 6, 857-869.Mallee, H. (1995). China’s household registration system under reform. Development and Change,

26, 1-29.Mansuri, G. (2006). Migration, sex bias, and child growth in rural Pakistan. World Bank Policy

Research Working Paper Series 3946.Mu, R., & van de Walle, D. (2009). Left-behind to farm? Women’s labor re-allocation in rural

China. World Bank Policy Research Working Paper No. 5107.Munshi, K. (2003). Networks in the modern economy: Mexican migrants in the US labor market.

Quarterly Journal of Economics, 118, 549-597.Nobles, J. (2007). Parental migration and child health in Mexico. Working paper, University of

California, Los Angeles.O’Donnell, O., van Doorslaer, E., Wagstaff, A. & Lindelow, M. (2008). Analyzing health equity

using household survey data. A Guide to Techniques and Their Implementation. Washington, DC: The World Bank.

Oaxaca, R. (1973). Male-Female wage differentials in urban labor markets. International Economic Review, 14, 693-709.

Peng, L. (2005). Survey on nutritional status of primary-middle school students and their social environment factors in Chongqing, China. Beijing Sport University: Doctor’s Thesis (in Chinese).

Schmeer, K. (2009). Father absence due to migration and child illness in rural Mexico. Social Science and Medicine, 69, 1281-1286.

Smith, J. (1999). Healthy bodies and thick wallets: the dual relation between health and economic status. Journal of Economic Perspectives, 13, 145-166.

Stark, O., & Taylorje, E. (1991). Migration incentives, migration types: the role of relative deprivation. The Economic Journal 101, 1163-1178.

Wooldridge, J.M. (2002). Introductory econometrics: a modern approach (Second Edition). Tsinghua University Press. pp. 585-593.

World Bank (2009). From Poor Areas to Poor People: China's Evolving Poverty Reduction Agenda. Washington, DC, World Bank.

Zhang, L., de Brauw, A., & Rozelle, S. (2004). China's rural labor market development and its gender implications. China Economic Review, 15, 230-247.